The way you are examining the BB off the bike is misleading. That center section is just a spacer - it doesn't hold the bearings in place and will move when it isn't in the bike. Same thing with the cup - it is designed to wedge the bearing, not necessarily hold it perfectly concentric unmounted. The only way to evaluate this BB is to mount it in a solid BB shell at full torque with grease inside and outside the cups.

Which brings us to the next issue - is your eccentric shell insert stiff enough to support the BB at full torque? When you turn the eccentric to (I assume) tighten the chain, are both sides actually moving perfectly together? Or is there some twisting that allows the BB to twist out of perpendicular with the bike? Would a different set up method help, like presetting the eccentric offset? With the eccentric completely locked, does the BB seem perfectly concentric on the NDS when you have the drive side tight?

I'm afraid your problem is too many moving parts and misalignments. If you have another frame with a normal BB, stick this in it and see if the problem remains.